What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 6001 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
| 6002 | 81254^33+33^81254 | 123386 | Hans Havermann | 03/2021 |
| 6003 | 33463^4854+4854^33463 | 123348 | Hans Havermann | 03/2021 |
| 6004 | 34061^4182+4182^34061 | 123348 | Hans Havermann | 03/2021 |
| 6005 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
| 6006 | L(2*409661)%(2^409661) | 123320 | Henri Lifchitz | 06/2025 |
| 6007 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
| 6008 | (82*10^123299+377)/9 | 123300 | Robert Price | 03/2022 |
| 6009 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
| 6010 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
| 6011 | 2^409436-112799 | 123253 | Enzo Doria | 06/2014 |
| 6012 | 28212^23321+23321^28212 | 123223 | Hans Havermann | 03/2021 |
| 6013 | 2^409225+1873787 | 123189 | Enzo Doria | 06/2016 |
| 6014 | 2^409174+73009 | 123174 | Enzo Doria | 04/2016 |
| 6015 | (4893*35^79754-31)/34 | 123148 | Eric Chen | 05/2025 |
| 6016 | 2^409058-112685 | 123139 | Enzo Doria | 06/2014 |
| 6017 | (13*10^123137-61)/3 | 123138 | Robert Price | 11/2018 |
| 6018 | 4*10^123113+21 | 123114 | Robert Price | 12/2018 |
| 6019 | 2^408778+77689 | 123055 | Enzo Doria | 05/2016 |
| 6020 | 660^43643-43643^660 | 123054 | Norman Luhn | 10/2024 |
| 6021 | 2^408690-75 | 123028 | Lelio R Paula | 11/2013 |
| 6022 | 28327^22032+22032^28327 | 123026 | Hans Havermann | 03/2021 |
| 6023 | (29*10^122996+673)/9 | 122997 | Robert Price | 12/2018 |
| 6024 | (65*10^122994-101)/9 | 122995 | Robert Price | 01/2022 |
| 6025 | 2^408574-2787341 | 122994 | Enzo Doria | 03/2016 |
| 6026 | 3*10^122977+37 | 122978 | Robert Price | 08/2018 |
| 6027 | (7*10^122976-67)/3 | 122977 | Robert Price | 10/2021 |
| 6028 | Phi(157825,10) | 122961 | Maksym Voznyy | 06/2015 |
| 6029 | 25493^27902-27902^25493 | 122948 | Frank Doornink | 02/2024 |
| 6030 | 26749^27768-27768^26749 | 122938 | Frank Doornink | 03/2024 |
| 6031 | (68*10^122933-419)/9 | 122934 | Robert Price | 07/2019 |
| 6032 | 29712^13721+13721^29712 | 122931 | Hans Havermann | 03/2021 |
| 6033 | (13*2^408283+1)/1665 | 122904 | Lelio R Paula | 05/2014 |
| 6034 | (266*10^122872-17)/3 | 122874 | Robert Price | 07/2020 |
| 6035 | (16*10^122871+77)/3 | 122872 | Robert Price | 03/2019 |
| 6036 | 30395^11022+11022^30395 | 122865 | Hans Havermann | 03/2021 |
| 6037 | 4*10^122859-69 | 122860 | Robert Price | 01/2022 |
| 6038 | (10^122857+167)/3 | 122857 | Robert Price | 05/2021 |
| 6039 | 33331^4852+4852^33331 | 122856 | Hans Havermann | 03/2021 |
| 6040 | (11*2^408100-1)/35 | 122850 | Lelio R Paula | 04/2014 |
| 6041 | (19*10^122836-43)/3 | 122837 | Robert Price | 05/2019 |
| 6042 | 315^49162-49162^315 | 122822 | Norman Luhn | 10/2024 |
| 6043 | 28420^20969+20969^28420 | 122820 | Hans Havermann | 03/2021 |
| 6044 | (16*10^122818+179)/3 | 122819 | Robert Price | 11/2021 |
| 6045 | 29865^12934+12934^29865 | 122797 | Hans Havermann | 03/2021 |
| 6046 | (2^407821-lucasV(1,2,407821)+1)/2 | 122767 | Mike Oakes | 11/2016 |
| 6047 | 17^99766+18 | 122757 | Anonymous | 09/2024 |
| 6048 | (32*10^122733-77)/9 | 122734 | Robert Price | 06/2018 |
| 6049 | (21*2^407604-1)/215 | 122701 | Lelio R Paula | 04/2014 |
| 6051 | (22*10^122681+161)/3 | 122682 | Robert Price | 05/2019 |
| 6050 | 29513^14350+14350^29513 | 122682 | Hans Havermann | 03/2021 |
| 6052 | (21*2^407433-1)/13 | 122650 | Lelio R Paula | 04/2014 |
| 6053 | Phi(149534,2^7) | 122640 | Henri Lifchitz | 10/2025 |
| 6055 | (26*10^122625-131)/3 | 122626 | Robert Price | 10/2019 |
| 6054 | (643*33^80753+3709)/32 | 122626 | Eric Chen | 12/2023 |
| 6056 | 27925^24562+24562^27925 | 122599 | Hans Havermann | 03/2021 |
| 6057 | (92365^24691-1)/92364 | 122599 | Anonymous | 09/2025 |
| 6058 | (73*10^122592-1)/9 | 122593 | Robert Price | 01/2015 |
| 6059 | (5*10^122592+91)/3 | 122593 | Robert Price | 04/2018 |
| 6060 | 36751^2166+2166^36751 | 122589 | Hans Havermann | 03/2021 |
| 6061 | (85*10^122585-1)/3 | 122587 | Robert Price | 02/2020 |
| 6062 | 29368^14931+14931^29368 | 122585 | Hans Havermann | 03/2021 |
| 6063 | 2^407179-112075 | 122574 | Enzo Doria | 06/2014 |
| 6064 | (21*2^407131+1)/207517523 | 122552 | Lelio R Paula | 04/2014 |
| 6065 | (66^67349+1)/67 | 122543 | Paul Bourdelais | 09/2017 |
| 6066 | (646*10^122533+11)/9 | 122535 | Robert Price | 10/2021 |
| 6067 | 2^407008-1867919 | 122522 | Enzo Doria | 04/2016 |
| 6068 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
| 6069 | (F(3*97700+1)^2+L(3*97700+1)^2)/2 | 122509 | Henri Lifchitz | 10/2017 |
| 6070 | 2^406949+72197 | 122504 | Enzo Doria | 04/2016 |
| 6071 | (19*10^122501+149)/3 | 122502 | Robert Price | 05/2019 |
| 6072 | 28632^18977+18977^28632 | 122495 | Hans Havermann | 03/2021 |
| 6073 | 31815^7076+7076^31815 | 122481 | Hans Havermann | 03/2021 |
| 6074 | 2^406826-65 | 122467 | Lelio R Paula | 11/2013 |
| 6075 | 2^406821-2797363 | 122466 | Enzo Doria | 04/2016 |
| 6076 | (7*10^122456-331)/9 | 122456 | Robert Price | 03/2022 |
| 6077 | 2^406758-17 | 122447 | Lelio R Paula | 11/2013 |
| 6078 | 29941^12282+12282^29941 | 122437 | Hans Havermann | 03/2021 |
| 6079 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
| 6080 | 27496^27577+27577^27496 | 122422 | Norbert Schneider | 12/2020 |
| 6081 | 28732^18215+18215^28732 | 122411 | Hans Havermann | 03/2021 |
| 6082 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
| 6083 | 4*10^122377+19 | 122378 | Robert Price | 10/2018 |
| 6084 | 28227^21634+21634^28227 | 122368 | Hans Havermann | 03/2021 |
| 6085 | Phi(246362,10) | 122365 | Makoto Kamada | 09/2019 |
| 6086 | 3*10^122345-97 | 122346 | Robert Price | 07/2018 |
| 6087 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
| 6088 | 2*10^122319+47 | 122320 | Robert Price | 12/2021 |
| 6089 | 208^52765+52765^208 | 122313 | Norbert Schneider | 11/2020 |
| 6091 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
| 6090 | 2^406296+213691 | 122308 | Enzo Doria | 09/2023 |
| 6092 | 7*10^122294+57 | 122295 | Robert Price | 06/2019 |
| 6093 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
| 6094 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
| 6095 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
| 6096 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
| 6097 | 29308^14835+14835^29308 | 122253 | Hans Havermann | 03/2021 |
| 6098 | 28119^22268+22268^28119 | 122253 | Hans Havermann | 03/2021 |
| 6099 | 32167^6312+6312^32167 | 122240 | Hans Havermann | 03/2021 |
| 6100 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
| 6101 | 27678^26053+26053^27678 | 122223 | Hans Havermann | 03/2021 |
| 6102 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
| 6103 | (8*10^122203+43)/3 | 122204 | Robert Price | 06/2018 |
| 6104 | (58*10^122170+329)/9 | 122171 | Robert Price | 05/2019 |
| 6105 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
| 6106 | 2^405693+20417 | 122126 | Enzo Doria | 07/2023 |
| 6107 | (218*10^122109+7)/9 | 122111 | Robert Price | 06/2022 |
| 6108 | 29189^15246+15246^29189 | 122103 | Hans Havermann | 03/2021 |
| 6110 | 34*10^122082-9 | 122084 | Robert Price | 06/2020 |
| 6109 | 33442^4473+4473^33442 | 122084 | Hans Havermann | 03/2021 |
| 6111 | 5*10^122082+41 | 122083 | Robert Price | 03/2019 |
| 6112 | 31849^6808+6808^31849 | 122078 | Hans Havermann | 03/2021 |
| 6114 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
| 6115 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |
| 6113 | 23*10^122070-7 | 122072 | Robert Price | 02/2020 |
| 6116 | 2^405422-113261 | 122045 | Enzo Doria | 07/2014 |
| 6117 | 95^61698-61698^95 | 122022 | Norman Luhn | 10/2024 |
| 6118 | 2^405173+71237 | 121970 | Enzo Doria | 04/2016 |
| 6119 | fibonacci(583574)+2 | 121960 | Jon Grantham | 08/2023 |
| 6120 | (154*10^121953+17)/9 | 121955 | Robert Price | 06/2022 |
| 6121 | (34*10^121924+191)/9 | 121925 | Robert Price | 08/2021 |
| 6122 | (2^405016+1)/257 | 121920 | Lelio R Paula | 04/2014 |
| 6123 | 28557^18590+18590^28557 | 121918 | Hans Havermann | 03/2021 |
| 6124 | 28641^18002+18002^28641 | 121877 | Hans Havermann | 03/2021 |
| 6125 | 2^404858+71329 | 121875 | Enzo Doria | 04/2016 |
| 6126 | 2^404813-114703 | 121861 | Enzo Doria | 04/2015 |
| 6127 | 2^404764+77791 | 121847 | Enzo Doria | 05/2016 |
| 6128 | 28830^16841+16841^28830 | 121847 | Hans Havermann | 03/2021 |
| 6129 | (4*10^121825+89)/3 | 121826 | Robert Price | 08/2021 |
| 6130 | 317^48694+48694^317 | 121787 | Norbert Schneider | 08/2015 |
| 6131 | 2^404536-115259 | 121778 | Enzo Doria | 06/2015 |
| 6132 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
| 6133 | 5*10^121764-69 | 121765 | Robert Price | 02/2021 |
| 6134 | (34^79493-3^79493)/31 | 121741 | Robert Price | 07/2025 |
| 6135 | 28236^20485+20485^28236 | 121738 | Hans Havermann | 02/2021 |
| 6136 | (382*10^121694-31)/9 | 121696 | Robert Price | 06/2022 |
| 6137 | 63^67620+2 | 121672 | Lelio R Paula | 08/2015 |
| 6138 | (25*34^79445-28062367)/33 | 121669 | Eric Chen | 08/2023 |
| 6139 | (13*33^80110-121453)/32 | 121648 | Eric Chen | 12/2023 |
| 6140 | (16*10^121633+167)/3 | 121634 | Robert Price | 06/2019 |
| 6141 | 29955^11494+11494^29955 | 121632 | Hans Havermann | 02/2021 |
| 6142 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
| 6143 | 31088^8163+8163^31088 | 121612 | Hans Havermann | 02/2021 |
| 6144 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
| 6145 | (211^52301-1)/210 | 121560 | Anonymous | 04/2024 |
| 6146 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
| 6147 | 801^41852-41852^801 | 121523 | Norman Luhn | 10/2024 |
| 6148 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
| 6149 | (41^75337-1)/98233421080 | 121492 | Paul Vanderveen | 05/2025 |
| 6150 | 715^42564-42564^715 | 121491 | Norman Luhn | 10/2024 |
| 6151 | (7*10^121487+143)/3 | 121488 | Robert Price | 03/2018 |
| 6152 | 27965^22086+22086^27965 | 121484 | Hans Havermann | 02/2021 |
| 6153 | (893*10^121470+7)/9 | 121472 | Robert Price | 06/2021 |
| 6154 | (206*10^121462-11)/3 | 121464 | Robert Price | 02/2022 |
| 6155 | 26282^27481-27481^26282 | 121457 | Frank Doornink | 03/2024 |
| 6156 | (77*10^121455+67)/9 | 121456 | Robert Price | 12/2021 |
| 6157 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
| 6158 | 25531^27552-27552^25531 | 121424 | Frank Doornink | 02/2024 |
| 6159 | (17*10^121418-113)/3 | 121419 | Robert Price | 06/2021 |
| 6160 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
| 6161 | 27929^22186+22186^27929 | 121382 | Hans Havermann | 02/2021 |
| 6162 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
| 6163 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
| 6164 | (873^41263+1)/874 | 121353 | Jinyuan Wang | 12/2024 |
| 6165 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
| 6166 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
| 6167 | 29404^13385+13385^29404 | 121340 | Hans Havermann | 02/2021 |
| 6168 | 28106^20745+20745^28106 | 121332 | Hans Havermann | 02/2021 |
| 6169 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
| 6170 | (23*10^121320-71)/3 | 121321 | Robert Price | 07/2020 |
| 6171 | 2^403004+1866361 | 121317 | Enzo Doria | 03/2016 |
| 6172 | 2^402953+89 | 121301 | Lelio R Paula | 10/2013 |
| 6173 | 2^402944-2788319 | 121299 | Enzo Doria | 03/2016 |
| 6174 | (44*10^121297-719)/9 | 121298 | Robert Price | 12/2018 |
| 6175 | (27*2^402865+1)/5 | 121276 | Lelio R Paula | 04/2014 |
| 6176 | 2^402828-113183 | 121264 | Enzo Doria | 07/2014 |
| 6177 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
| 6178 | (15*2^402757+1)/101 | 121242 | Lelio R Paula | 05/2014 |
| 6179 | 282^49477-49477^282 | 121231 | Norman Luhn | 10/2024 |
| 6181 | 2^402715+1874223 | 121230 | Enzo Doria | 06/2016 |
| 6180 | (35*10^121229-593)/9 | 121230 | Robert Price | 07/2018 |
| 6182 | (91^61879+1)/92 | 121222 | Paul Bourdelais | 09/2017 |
| 6183 | 291^49190-49190^291 | 121199 | Norman Luhn | 10/2024 |
| 6184 | (10^121243)/(121243^10) | 121193 | Henri Lifchitz | 05/2025 |
| 6185 | 28719^16568+16568^28719 | 121174 | Hans Havermann | 02/2021 |
| 6186 | 7*10^121144+9 | 121145 | Robert Price | 09/2015 |
| 6187 | 27490^25467+25467^27490 | 121121 | Hans Havermann | 02/2021 |
| 6188 | 34575^3182+3182^34575 | 121106 | Hans Havermann | 02/2021 |
| 6189 | 5*10^121100-37 | 121101 | Robert Price | 11/2021 |
| 6190 | F(579521)/516247738177 | 121101 | Serge Batalov | 07/2024 |
| 6191 | 25592^27467-27467^25592 | 121078 | Frank Doornink | 02/2024 |
| 6192 | 29954^10935+10935^29954 | 120979 | Hans Havermann | 02/2021 |
| 6193 | 33585^3992+3992^33585 | 120946 | Hans Havermann | 02/2021 |
| 6194 | 40296^1003+1003^40296 | 120941 | Hans Havermann | 02/2021 |
| 6195 | 2^401725-113251 | 120932 | Enzo Doria | 07/2014 |
| 6196 | (15*2^401677-1)/19 | 120917 | Lelio R Paula | 05/2014 |
| 6197 | 2^401652+73711 | 120910 | Enzo Doria | 04/2016 |
| 6198 | (2^401632+3)/79 | 120902 | Lelio R Paula | 04/2014 |
| 6199 | 40450^973+973^40450 | 120870 | Hans Havermann | 01/2021 |
| 6200 | (8*10^120851-11)/3 | 120852 | Robert Price | 07/2023 |
| 6201 | 10^120841+88417 | 120842 | Patrick De Geest | 04/2020 |
| 6202 | 10^120841-123456789 | 120841 | Robert Price | 02/2020 |
| 6203 | 10^120841-176853 | 120841 | Patrick De Geest | 04/2020 |
| 6204 | 2^401406-2791331 | 120836 | Enzo Doria | 03/2016 |
| 6205 | (28^83497+1)/29 | 120832 | Robert Price | 07/2013 |
| 6206 | (22*10^120828+161)/3 | 120829 | Robert Price | 05/2019 |
| 6207 | 2^401369+1867367 | 120825 | Enzo Doria | 03/2016 |
| 6208 | (5*10^120821+43)/3 | 120822 | Robert Price | 12/2021 |
| 6209 | 26990^27263-27263^26990 | 120808 | Frank Doornink | 03/2024 |
| 6210 | (10^120782+29)/3 | 120782 | Serge Batalov | 12/2014 |
| 6211 | 2^401215-1657 | 120778 | Yves Minet | 07/2014 |
| 6212 | 2^401159+53 | 120761 | Lelio R Paula | 10/2013 |
| 6213 | 27782^22179+22179^27782 | 120739 | Hans Havermann | 01/2021 |
| 6214 | 242^50649-50649^242 | 120738 | Norman Luhn | 09/2024 |
| 6215 | 32974^4585+4585^32974 | 120730 | Hans Havermann | 02/2021 |
| 6216 | 2^401031-113047 | 120723 | Enzo Doria | 07/2014 |
| 6217 | 30598^8813+8813^30598 | 120713 | Hans Havermann | 02/2021 |
| 6218 | (71*10^120703-287)/9 | 120704 | Robert Price | 09/2019 |
| 6219 | 25671^27370-27370^25671 | 120687 | Frank Doornink | 02/2024 |
| 6220 | (29*2^400909-1)/303 | 120685 | Lelio R Paula | 04/2014 |
| 6221 | 34793^2940+2940^34793 | 120675 | Hans Havermann | 02/2021 |
| 6222 | 26028^27329-27329^26028 | 120670 | Frank Doornink | 03/2024 |
| 6223 | (2^400846+538)/2 | 120667 | Stefano Morozzi | 09/2020 |
| 6224 | (166*10^120654+11)/3 | 120656 | Robert Price | 03/2021 |
| 6225 | 34066^3481+3481^34066 | 120652 | Hans Havermann | 02/2021 |
| 6226 | 8*10^120637-27 | 120638 | Robert Price | 10/2021 |
| 6227 | (2^400709+3546)/2 | 120626 | Stefano Morozzi | 09/2020 |
| 6228 | (2^400700+3126)/2 | 120623 | Stefano Morozzi | 09/2020 |
| 6229 | (2^400693+2634)/2 | 120621 | Stefano Morozzi | 09/2020 |
| 6230 | 9*10^120617-61 | 120618 | Robert Price | 06/2021 |
| 6231 | (29*10^120590-71)/3 | 120591 | Robert Price | 07/2021 |
| 6232 | 2^400571-15 | 120584 | Lelio R Paula | 10/2013 |
| 6233 | (10^120574+359)/9 | 120574 | Serge Batalov | 12/2014 |
| 6234 | (8*10^120552-17)/9 | 120552 | Serge Batalov | 11/2022 |
| 6235 | 27431^24810+24810^27431 | 120550 | Hans Havermann | 02/2021 |
| 6236 | 2^400424-216413 | 120540 | Enzo Doria | 04/2013 |
| 6237 | 29090^13911+13911^29090 | 120531 | Hans Havermann | 02/2021 |
| 6238 | (2^400346+1722)/2 | 120516 | Stefano Morozzi | 09/2020 |
| 6239 | 27899^20868+20868^27899 | 120510 | Hans Havermann | 02/2021 |
| 6240 | 33740^3729+3729^33740 | 120506 | Hans Havermann | 02/2021 |
| 6241 | (17*2^400200-1)/587 | 120471 | Lelio R Paula | 05/2014 |
| 6242 | 17228^28437-28437^17228 | 120466 | Norbert Schneider | 08/2025 |
| 6243 | 1069^39770-39770^1069 | 120463 | Norbert Schneider | 05/2025 |
| 6245 | 2^400166+1874899 | 120462 | Enzo Doria | 06/2016 |
| 6244 | (2^400165+1602)/2 | 120462 | Stefano Morozzi | 09/2020 |
| 6246 | 2739^35038-35038^2739 | 120447 | Norbert Schneider | 05/2025 |
| 6247 | 37078^1771+1771^37078 | 120438 | Hans Havermann | 02/2021 |
| 6248 | (2^400084+1638)/2 | 120437 | Stefano Morozzi | 09/2020 |
| 6249 | (3*2^400045-1)/865 | 120424 | Lelio R Paula | 04/2014 |
| 6250 | 12857^29306-29306^12857 | 120423 | Norbert Schneider | 07/2025 |
